Shall moderators move obviously misplaced postings?

That question (as well as some explanation and maybe even an answer) would be better placed here ...

I'd suggest that the moderators move misplaced postings to matching threads if it is clear that the intention of the poster is better off in the other (new) thread (like in the example above) and inform the poster - "your posting has been moved..."

Possibly even move to a new thread if it is obvious that it is a benefit for the poster...

For other, possibly misplaced postings, ask the poster to move the posting her/himself, like in the example above...